System and methods for wavefront measurement

ABSTRACT

A method and apparatus for characterizing an object with a wavefront from the object is disclosed. In one embodiment, the apparatus includes: a reticle positioned in a path of the wavefront, the reticle comprising two superimposed linear grating patterns; at least one light detector positioned relative to the reticle to receive a self-image diffraction pattern of the reticle produced by the wavefront; and at least one processor receiving signals from the light detector representative of the self-image diffraction pattern and deriving derivatives associated therewith, the processor using the derivatives to characterize said object.

RELATED APPLICATION INFORMATION

This application is a continuation of U.S. patent application No.10/314,906, filed Dec. 9, 2002, which is a continuation-in-part of U.S.patent application No. 10/014,037, filed Dec. 10, 2001, now U.S. Pat.No. 6,781,681, each of which are hereby incorporated by reference intheir entireties.

FIELD OF THE INVENTION

The present invention relates generally to systems and methods formeasuring phase characteristics of electromagnetic wavefronts.

BACKGROUND

Measuring how a wavefront deviates from being perfectlydiffraction-limited has many applications. As non-limiting examples,measuring deviations, also referred to as “aberrations”, in a wavefrontproduced by an optical system, such as a telescope, can revealmanufacturing flaws in the system, since many optical systems, tofunction as best as is possible, preferably produce diffraction-limitedwavefronts. By adding a component to the system that produces awavefront that is the conjugate of the measured deviations, the systemcan be made to produce a more diffraction-limited wavefront and, thus,diffraction-limited performance (i.e., best possible performance).

Another example of an application where knowing the aberrations in awavefront is useful is in correcting human vision. For instance, asnoted in U.S. Pat. No. 5,963,300, by measuring deviations from theperfectly spherical in reflections of laser light from the eye of apatient, aberrations of the eye can be measured and, hence, compensatedfor. In the '300 patent, light that is reflected from a patient's eye ispassed through two reticles, and the resulting moire shadow pattern ispresented on a screen. An imaging system images the shadow on the screenonto a camera, with subsequent analysis being undertaken of the imagedshadow. The technique of the '300 patent is based on geometrical orray-tracing analysis, which as recognized herein requires theoreticalassumptions to perform the geometrical analysis that limit the amplitudeof the aberrations that can be measured as well as limit the accuracywith which the aberrations can be measured.

Certain embodiments of the technology discussed below may providesolutions to one or more of these drawbacks.

SUMMARY OF THE INVENTION

A system for determining aberrations in a coherent electromagneticwavefront includes a reticle that is positioned in the path of thewavefront, and a detector also positioned in the path. In accordancewith this aspect, the light detector is located at a diffraction patternself-imaging plane or Talbot plane relative to the reticle.

A processor may receive the output signal from the light detector anddetermine aberrations in the beam based thereon. The aberrations in thebeam may represent aberrations in the wavefront due to the mediumthrough which it passes, or an object from which it reflects, or thesource of the wavefront itself.

In a preferred, non-limiting embodiment, the processor executes logicthat includes determining a phase gradient of the wavefront phase-front,and determining coefficients of polynomials based on the phase-frontgradient which quantify the aberrations. The coefficients representaberrations. Preferably, the gradient is obtained from a frequencydomain transformation of the beam, wherein the gradient is thederivative of the phase of the wavefront in directions established bythe reticle orientation. In a particularly preferred, non-limitingembodiment, the derivatives are determined in at least two directions,and the coefficients are determined by fitting derivatives of a set ofknown polynomials (such as e.g. Zernike polynomials) to the measuredgradient.

In another aspect, a method for determining aberrations in an objectincludes passing a light beam from the object through a reticle, andthen determining derivatives that are associated with the light beamsubsequent to the light beam passing through the reticle. Using thederivatives, a measure of aberrations in the object can be output.

In yet another aspect, a computer program product includes a computerreadable medium having a program of instructions stored thereon forcausing a digital processing apparatus to execute method steps fordetermining aberrations in a wavefront. These method steps includerepresenting a diffraction pattern produced by a wavefront, anddetermining directional derivatives of the representation. Thederivatives are fit to known polynomials or derivatives thereof toobtain coefficients of polynomials. A wavefront characterization isprovided based at least in part on the coefficients, with the wavefrontcharacterization representing aberrations in the wavefront. A frequencydomain representation of the image produced by the wavefront may also begenerated. Furthermore, the directional derivatives may be determined intwo directions.

In still another aspect, an apparatus for detecting aberrations in anobject as manifested in a wavefront includes a reticle positioned in apath of the wavefront and a light detector positioned relative to thereticle to receive the diffracted self-image that is associated with thewavefront. The self-imaging distances are at discrete distances from thereticle that are integral multiples of

${d = \left( \frac{n\; p^{2}}{\lambda} \right)},$where p is the period of the reticle and λ is the spectral wavelength ofthe wavefront. A processor receives signals from the light detector thatrepresent the self-image. The processor derives the wavefront phasegradient associated with the wavefront and uses the coefficients ofderivatives of polynomials that define the wavefront to determine thewavefront aberrations.

Another aspect of the invention comprises a system for determining theshape of an electromagnetic wavefront. This system includes at least onereticle positioned in a path of the wavefront to be analyzed and atleast one detector positioned to detect the wavefront passing throughthe reticle. The detector is substantially located at a diffractionpattern self-imaging plane relative to the reticle. The system furthercomprises at least one processor receiving an output signal from thelight detector and calculating the shape of the wavefront based thereon.

Still another aspect of the invention comprises a method for determiningaberrations in an optical system comprising at least one opticalelement. In this method, a test beam is propagated along a path with theoptical system in the path of the test beam so as to be illuminated bythe test beam. A reticle is inserted in the path of the test beam at alocation with respect to the optical system so as to receive light fromthe optical system. The light propagates through the reticle.Directional derivatives associated with the light are determinedsubsequent to passing through the reticle. Additionally, the derivativesare used to output a measure of the aberrations.

Yet another aspect of the invention comprises a computer program productcomprising a computer readable medium having a program of instructionsstored thereon for causing a digital processing apparatus to executemethod steps for determining aberrations in a wavefront. These methodsteps include representing at least a portion of an image produced bythe wavefront and determining directional derivatives of therepresentation. In addition, directional derivatives are fit to knownpolynomials or derivatives thereof to obtain coefficients ofpolynomials. Furthermore, a wavefront characterization is provided basedat least in part on the coefficients, the wavefront characterizationrepresenting aberrations in the wavefront.

Still another aspect of the invention comprises an apparatus forcharacterizing an object with a wavefront from the object. The apparatusincludes at least one reticle positioned in a path of the wavefront andat least one light detector positioned relative to the reticle toreceive a self-image diffraction pattern of the reticle produced by thewavefront. The apparatus further includes at least one processorreceiving signals from the light detector representative of theself-image diffraction pattern and deriving derivatives associatedtherewith. The processor uses the derivatives to characterize theobject.

Another aspect of the invention comprises a method for determiningaberrations in a reflective or internally reflective object system. Inthis method, a light beam is passed from the object system through areticle. This light beam produces a near field diffraction pattern atthe Talbot plane. The method further comprises imaging the near fielddiffraction pattern at the Talbot plane and using the near fielddiffraction pattern to output a measure of aberrations in the lightbeam.

BRIEF DESCRIPTION OF THE DRAWINGS

The details of the various preferred embodiments, both as to theirstructure and operation, can best be understood in reference to theaccompanying drawings, in which like reference numerals refer to likeparts, and in which:

FIG. 1 is a block diagram of the one preferred embodiment of a systemarchitecture for measuring and characterizing a wavefront;

FIG. 1 a is a block diagram of another implementation of the systemshown in FIG. I;

FIG. 2 is a flow chart of a preferred method of characterizing thewavefront by propagating the wavefront through a pattern and imaging thepattern at the self-image plane;

FIGS. 3 a-3 c are schematic diagrams illustrating one method forconverting the image produced at the self-image plane into gradientinformation corresponding to the wavefront at that self-image plane;

FIG. 4 is a flow chart of preferred logic for data extraction in thespatial frequency domain; and

FIG. 5 is a flow chart of further logic for extraction of the desireddata from spatial frequency data.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring initially to FIG. 1, a wavefront sensor is shown, generallydesignated 10. As illustrated in FIG. 1, a reference wavefront 11 canpass through (or, be reflected from) a system or element 12 (optical orotherwise). The system or element 12 can be an optics system, such as atelescope system, or it can be a human eye, or other object havingproperties, e.g., aberrations or curvature, sought to be measured.

As shown in FIG. 1, a transferred wavefront 18, i.e., the wavefront 11after having passed through or having been reflected from the system orelement 12, passes through a reticle 20. For example, this reticle 20may comprise without limitation, a diffraction grating, Ronchi ruling,or grid pattern. The reticle 20 diffracts the wavefront 18, and thediffracted wavefront self-images onto a sensor plane a self-imagingdistance “d” away from the reticle 20 at which location is disposed alight sensor 22 such as but not limited to a CCD or other detectorarray. The self-imaging distance “d” is dependent on the spectralwavelength of the coherent wavefront and the spatial frequency of thereticle. Preferably, the CCD is within about .+−.10% or about .+−.20% ofone of the self-imaging planes in the near field diffraction region.

In a non-limiting, exemplary embodiment, the wavefront incident on theimaging detector can be represented by the following diffractionequation:

${I\left( {\overset{->}{r},z} \right)} = {I_{0}{\cos\left( \frac{{\pi\lambda}\; z}{p^{2}} \right)}{\cos\left\lbrack {\frac{2\pi}{p}\left( {{\overset{->}{r} \cdot \hat{p}} - {\hat{r} \cdot \left( {\overset{->}{z}\; X{\overset{->}{\nabla}w}} \right)}} \right)} \right\rbrack}}$

where: λ is the wavelength of the coherent wavefront, z is thepropagation distance with the associated vector {right arrow over (z)}in propagation direction, p is the period of the reticle (distance fromthe beginning of one grid line to the next grid line), r is the spatialdimension in the plane of the detector with its associated vector {rightarrow over (r)}, {circumflex over (r)} is the corresponding unit vector,{circumflex over (p)} the unit vector representing the reticleorientation, and {right arrow over (∇)} is the directional-derivative(or, gradient) of the wavefront phase “w” that is being measured. Theself-imaging distance is dependent on the spectral wavelength of thecoherent wavefront and the spatial frequency of the reticle and is givenby:

$d = \left( \frac{n\; p^{2}}{\lambda} \right)$

where n is the integer multiple at which distances the self-imagesoccurs. For example, for a reticle having a grating spacing, p, of 50micrometers (μm), this distance, d, may be between about 2.9 to 3.0millimeters (mm) or in proximity thereto for light having a wavelengthof 850 nanometers (nm). Integer multiples of this distance may beappropriate as well.

As described below, this reticle 20 may comprise rulings in orthogonal xand y directions having substantially the same period p. In otherembodiments, the spacing p_(x) and p_(y) of the orthogonal rulings maybe different for the x and y directions. Corresponding self-image planesat distances d_(x) and d_(y) for the different directed rulings mayresult. Similarly, use of more than one or two reticle patternssuperimposed on another having same or different periodicity areconsidered possible.

The self-imaged reticle on the light sensor or detector 22 that islocated at the self-image plane contains the desired informationpertaining to the phase characteristics of the coherent wavefront. Thisinformation is extracted from the spatial signal collected at the sensor22 and sent to a data processor (i.e., computer) 24 for processing inaccordance with the disclosure below. To undertake the logic, theprocessor 24 accesses a preferably software-implemented module 26, andoutputs a signal representative of the wavefront (or a conjugatethereof) to an output device 28, such as but not limited to a printer,monitor, computer, network, or other appropriate device.

In various embodiments, the beam that emerges from the reticle 20establishes a diffraction pattern. This pattern, however, substantiallycannot be discerned except at the self-image planes that are spacedinteger multiples of a distance “d” from the reticle 20, as discussedabove. Thus, the self image diffraction pattern can be detected by thelight sensor or detector 22 that in one preferred embodiment is placedat the first (n=1) self-image plane as shown in FIG. 1, although it isto be understood that the sensor or detector 22 can be positioned at anyof the self-image planes that are spaced from the reticle 20 by integermultiples of the distance “d”.

Logic may be executed on the architecture shown in FIG. 1 in accordancewith processes and methods described and shown herein. These methods andprocesses include, but are not limited to, those depicted in at leastsome of the blocks in the flow chart of FIG. 2 as well as the schematicrepresentations in FIGS. 3 a-3 c and flow charts in FIGS. 4 and 5. Theseand other representations of the methods and processes described hereinillustrate the structure of the logic of various embodiments of thepresent invention which may be embodied in computer program software.Moreover, those skilled in the art will appreciate that the flow chartsand description included herein illustrate the structures of logicelements, such as computer program code elements or electronic logiccircuits. Manifestly, various embodiments include a machine componentthat renders the logic elements in a form that instructs a digitalprocessing apparatus (that is, a computer, controller, processor, etc.)to perform a sequence of function steps corresponding to those shown.

In other words, the logic may be embodied by a computer program that isexecuted by the processor 24 as a series of computer- or controlelement-executable instructions. These instructions may reside, forexample, in RAM or on a hard drive or optical drive, or the instructionsmay be stored on magnetic tape, electronic read-only memory, or otherappropriate data storage device that can be dynamically changed orupdated.

FIG. 1 a shows a particular non-limiting implementation of the system 10in which the electromagnetic energy is reflected from an object or isinternally reflected from within an object. Examples of applicationsinclude microwave topography of large surfaces, wherein theelectromagnetic energy is microwave and the object is the surface soughtto be measured; optical topography of reflective surfaces, wherein theelectromagnetic energy is laser light; retinal reflection within an eyein order to measure the aberrations of the eye, and gamma ray reflectionwithin very small objects in order to characterize mechanical or opticalproperties.

Accordingly, for illustration purposes FIG. 1 a shows that the referencewavefront 11 passes through (or, is reflected from) a transfer (opticalor otherwise) system or element 15, such as but not limited to abeamsplitter, along a propagation path 13. The wavefront 11 is incidenton an object 12 such as a human eye wherein it is either reflectedexternally or transmits into the object 12 where it is internallyreflected. The return wavefront follows along a return path 17, and canbe reflected from or transmitted through the transfer system or element15. The wavefront may then pass through an optical relay system 19. Thetransferred wavefront 18 passes through the reticle 20 and is processedas described above in reference to FIG. 1.

The logic of the processor 24 can be appreciated in reference to FIG. 2.Commencing at block 30 in FIG. 2, the wavefront 18 of the beam passesthrough the reticle 20. Diffraction effects cause a self-image of thereticle to appear at the self-image planes described above, including atthe first plane located at a distance “d” from the reticle 20 where thedetector 22 is positioned. The particular plane chosen for the positionof the detector 22 preferably has sufficient resolution cells to resolvethe diffraction pattern.

The self-image diffraction pattern caused by the beam 18 passing throughthe reticle 20 is acquired at block 33 by the sensor or detector 22 andis represented by the signal output by the light detector 22, asreceived by the processor 24. Proceeding to block 34, the signal in thespatial image domain is transformed to the spatial frequency domain. Inone non-limiting embodiment, executing a Fast Fourier Transform (FFT) onthe signal performs this, although it is to be understood that othermathematical transformations can be used. While FIG. 2 indicates thatthe FFT is implemented in software, it is to be understood by thoseskilled in the art that alternatively, prior to being sent to theprocessor 24 an optical FFT of the return beam can be made using opticssuch as are known in the art.

Proceeding to block 36, regions of interest in the frequency domain maybe selected based on the reticle period, illumination (i.e.,wavelength), and other factors discussed further below. This selectioncan be a priori, and need not be undertaken during measurement.Essentially, at block 36 the regions of interest for which the gradient(directional derivative) of the wavefront is to be determined arelocated in the spatial frequency domain and isolated.

In various preferred embodiments, the portions of the spatial frequencydomain that contain the slope information and that consequently areisolated depend on the configuration of the reticle 20 and can be, e.g.,represented by distributions mapped on different places on orthogonalaxes in frequency space. Suitable spatial frequency domain manipulationis further illustrated in FIG. 3, discussed below.

Proceeding to block 38, an inverse transform is applied only to theisolated frequency space regions of the signal to render a spatialrepresentation of the gradient of the wavefront preferably in thedirection normal to the linear or segmented linear dimension of thereticle. Thus, if the reticle contains a singular set of linear gratinglines, there will be two regions of the spatial frequency domaincontaining the desired information. If there are two sets of lineargratings superimposed in the reticle, the spatial frequency domain willcontain four regions of interest. Each additional set of linear gratingsprovides more information pertaining to the wavefront gradient. In thelimit, a circular grating reticle represents an infinite number ofsegmented linear gratings superimposed on each other. Preferably, thereticle contains two orthogonal superimposed linear grating patterns. Ina non-limiting preferred embodiment, the wavefront gradient isdetermined in isolated regions in two directions. In a non-limitingexample, when the object 12 is a human eye, the two directions areorthogonal to each other and lie in a plane defined by the front of andtangential to the patient's eye, with one of the directions extendingfrom the center of the eye at a 45.degree. angle relative to thehorizontal and tangent to the eye when the, patient is standing andfacing directly forward.

If desired, in a non-limiting embodiment filtering of random backgroundnoise can be further applied by using a “computationally-implemented”matte screen by which the spatial characteristics of the self-image areenhanced and the background reduced to very low (e.g., approximatelyzero) frequency components in the spatial frequency domain. Thisprinciple will be further discussed in relation to FIG. 5.

Moving to block 40, a set of known functions such as polynomials (andtheir derivatives) is defined or otherwise accessed for the twodirections mentioned above. These polynomials can be used to model thewavefront. In one preferred, non-limiting embodiment, a set of 36Zernike polynomials are used. Then, at block 42 the derivatives of theknown polynomials are fit to the derivatives (i.e., gradient) determinedat block 38 using, e.g., a least squares fit or other fitting algorithm.

The outcome of the fitting step at block 42 is that each polynomial hasan accompanying coefficient, also referred to as the “amplitude” of thepolynomial. Each coefficient represents an aberration from the perfectlyspherical in the return beam 18 and, hence, an aberration in the object12. Consequently, at block 44 a reconstructed wavefront equation can beoutput (to, e.g., the output device 28) that is the set of the knownpolynomials with the coefficients obtained in the fitting step at block42. At block 46, the output, and in particular the coefficients in thereconstructed wavefront equation, can be used to indicate aberrations inthe original wavefront and, hence, in the object 12. Furthermore, theoutput can be used as a basis for implementing corrective optics for thesystem 12 that essentially represent the conjugate of the polynomialsand/or coefficients to reduce or null out the aberrations of the object12.

A schematic representation of an exemplary process for characterizing awavefront gradient is depicted in FIGS. 3 a-3 c. A spatial image 100 ofthe reticle at the detector located in the self-image plane is convertedby applying a Fourier transform, represented by block 102, into spatialfrequency data 104. The result, is a spatial frequency pattern thatincludes four regions of interest 106 a, 106 b, 106 c, and 106 d whichmay correspond to a set of first order components in frequency space.These four regions comprise point spread functions (PSF) displaced fromthe origin of the spatial frequency map in directions corresponding to±f_(x) and ±f_(y). As shown in block 108, one of these four regions isselected. In FIG. 3 b, the point spread function at the (+f_(x0)0)location is selected and the inverse Fourier transform is performed onthis spatial frequency distribution as represented by block 110. In thismanner, the gradient along the x direction of the wavefront at theself-image plane can be obtained as shown indicated by block 112.Similarly, FIG. 3 c shows the point spread function at the (0, +f_(y0))position in block 114. The inverse Fourier transform is performed onthis point spread function as represented by block 116 to obtain thegradient of the wavefront in the y direction shown in block 118.

FIG. 4 shows further details of this process as discussed with respectto blocks 34, 36 and 38 in FIG. 2. At block 50 in FIG. 4, the self-imageof the reticle is converted using software or optically from spatialdata to spatial frequency data. As discussed above, this is preferablyperformed with a Fourier Transform algorithm and preferably a FastFourier Transform computer software algorithm (FFT). Moving to block 52,from an a priori knowledge of the system 10 configuration, regions ofinterest in the spatial frequency domain are selected. The a prioriinformation is provided at block 54 as follows. The reticle 20 has (a)periodic pattern(s) in known directions. The period of the reticle, thenumber of superimposed reticles, and the spatial orientations of thereticle relative to the wavefront path of propagation can be used tolocate these regions. Gradient data in the individual regions ofinterest is accessed at block 56 and isolated at block 58. This data hassymmetry in the spatial frequency domain. Accordingly, in block 60 ifdesired only one of the symmetric data sets need be selected. Then inblock 62 each set is converted back to the spatial domain. The offset ofthe location in frequency space of the “first order” region of interestmay be used to calibrate the gradient information. This process ofobtaining the wavefront phase gradient information is included in block38 in FIG. 2.

Without subscribing to any particular scientific theories, the aboveoperations by which the wavefront is extracted from equation (1) can beexpressed in analytical form as follows. First, the non-limiting Fouriertransform on the wavefront executed at block 50 in FIG. 4 can beexpressed as:

$\left. {F\left\{ {l\left( {r,z} \right)} \right\}\begin{matrix}{{f^{2}x},y} & {{f^{4}x},y} \\{{f^{1}x},y} & {{f^{3}x},y}\end{matrix}}\Rightarrow{F\left( {\nabla w} \right)} \right.$

wherein the notation f¹x,y, f²x,y, f³x,y and f⁴x,y indicates that incertain embodiments described above such as illustrated in FIGS. 3 a-3c, the relevant frequency information obtained by the Fourier transformis contained in four first order distributions or point spread functions106 a, 106 b, 106 c, 106 d located in four sectors in frequency space.Similarly, the two spatial frequency regions f¹x,y to f²x,y and f³x,y tof⁴x,y are the two dimensional areas in the frequency domain that containthe relevant data, and F(∇w) represents the received wavefront. Thelocation of the point spread function may vary in different embodiments.

Then, the gradient (∇w) of the wavefront is determined by performing theinverse Fourier transform (F⁻¹) on equation (3) as follows:F⁻¹{F(∇w)}

∇w

Next, the set of partial derivatives, or gradients, of the chosenpolynomial set, e.g., Zernike polynomials (∇Z, or Z_(x) and Z_(y)) aremade to best approximate the gradient of the phase front (∇w) via one ormore fitting algorithms such as for example a least squares algorithm.That is.

${\nabla w} = {\sum\limits_{i = 1}^{n}{A_{i}Z_{i}}}$

where, n is the number of polynomials chosen to best approximate thewavefront phase gradient, and A_(i) is the coefficient, or amplitude, ofthe polynomial Z_(i). The wavefront phase “w” can now be described asfollows:

$w = {\sum\limits_{i = 1}^{n}{A_{i}Z_{i}}}$

The aberrations in the wavefront can be described by the values of thecoefficients A_(i).

The flow chart of FIG. 5 shows the process of the“computationally-implemented” matte screen discussed above in relationto FIG. 2. In a monochromatic system a high pass spectral filter may beused to eliminate signal noise. In one exemplary embodiment, this filteris a piece of hardware called a matte screen. In many applications amatte screen is not practical to integrate into the system. Accordingly,the matte screen can be computationally implemented on the self-images.

The contrast of the image and the self-image fundamental spatialfrequency are respectively received from blocks 70 and 71 and input toblock 72, where the two inputs are compared to discriminate theself-image signal. If the contrast from block 70 is lower than thefundamental spatial frequency from block 71, the matte screen isimplemented within block 34 of FIG. 2, with the location of the peakvalue in the region of interest in block 38 providing the fundamental(predominant) frequency within the self-image signal. From the peak, afinite impulse response (FIR) kernel is derived at block 74 thatfunctions as a high-pass filter of spatial frequency data. Onlyfrequencies higher then the designed limit will remain in the signal,and all others are eliminated at block 76 by mathematically convolvingthe kernel with the self-image signal.

By employing methods such as described above, a mathematicalrepresentation of the wavefront and of the aberrations can be obtained.Additionally, conjugate structures, e.g., conjugate optics, can becreated to substantially offset or cancel the aberrations in thewavefront. In the case, for example, where the wavefront in the eye ismeasured, these conjugate optics, e.g., may take the form of acorrective lens and the method of measuring the wavefront describedabove can be employed to determine the appropriate prescription for sucha lens.

Those skilled in the art will appreciate that the methods and designsdescribed above have additional applications and that the relevantapplications are not limited to those specifically recited above. Also,the present invention may be embodied in other specific forms withoutdeparting from the essential characteristics as described herein. Theembodiments described above are to be considered in all respects asillustrative only and not restrictive in any manner.

1. A system for determining aberrations in an electromagnetic wavefront,comprising: at least one source of the electromagnetic wavefrontdirecting a beam onto an object system, the object system reflecting orpassing at least part of the beam to render a wavefront to be analyzed;a reticle positioned in a path of the wavefront to be analyzed, whereinthe reticle comprises two superimposed linear grating patterns; at leastone detector positioned to detect the wavefront passing through thereticle, the detector being located at a diffraction patternself-imaging plane relative to the reticle; and at least one processorreceiving an output signal from the light detector and determining atleast one aberration in the wavefront based thereon, the aberrationrepresenting at least one aberration in the object system, wherein theprocessor executes logic to undertake method acts comprising: a.accessing mathematical functions to characterize the electromagneticwavefront; and b. determining directional derivatives of theelectromagnetic wavefront using the mathematical functions.
 2. Thesystem of claim 1, wherein at least one of the two superimposed lineargrating patterns is segmented.
 3. The system of claim 2, wherein the twosuperimposed linear grating patterns are orthogonal with respect to oneanother.
 4. The system of claim 1, wherein the object system is an eye.5. The system of claim 4 wherein the two superimposed linear gratingpatterns are orthogonal with respect to one another and liesubstantially in a vertical plane, and wherein the reticle is rotated inthe vertical plane at approximately a 45° angle from a horizontal plane.6. The system of claim 4, wherein the wavefront incident on the eye istransmitted into the eye and reflected internally, creating a returnwavefront, the return wavefront exiting the eye.
 7. The system of claim1, wherein the method acts include determining coefficients ofpolynomials based on at least one gradient of a phase-front of thewavefront, the coefficients being representative of aberrations.
 8. Thesystem of claim 7, wherein the method acts further comprise transformingthe wavefront from a spatial image domain into a spatial frequencydomain, prior to the act of determining coefficients.
 9. The system ofclaim 8, wherein only selected portions in the spatial frequency domainare used to determine coefficients.
 10. The system of claim 8, whereinthe act of determining coefficients includes determiningdirectional-derivatives of phases of the wavefront.
 11. The system ofclaim 10, wherein directional derivatives are determined in at least twodirections.
 12. The system of claim 11, wherein the coefficients aredetermined by fitting derivative functions of a set of known polynomialsto the derivatives obtained during the determining act.
 13. A method fordetermining aberrations in an object system, comprising: a. passing alight beam from the object system through a reticle, wherein the reticlecomprises two superimposed linear grating patterns: b. transforming awavefront associated with the light beam from a spatial image domaininto a spatial frequency domain; c. determining directional derivativesassociated with the light beam subsequent to the light beam passingthrough the reticle; and d. determining coefficients of polynomialsbased on the directional derivatives, wherein the derivatives are usedto output a measure of abenations in the light beam.
 14. The method ofclaim 13, wherein at least one of the two superimposed linear gratingpatterns is segmented.
 15. The method of claim 12, wherein the twosuperimposed linear grating patterns are orthogonal with respect to oneanother and form a checkerboard pattern.
 16. The method of claim 13,wherein the act of determining derivatives includes determiningderivatives of phases of the wavefront.
 17. The method of claim 13,comprising determining directional derivatives in at least twodirections.
 18. The method of claim 13, wherein the coefficients aredetermined by fitting derivatives of a set of known polynomials to dataobtained during the determining act.
 19. The method of claim 13, whereinthe object system is an eye.
 20. The method of claim wherein the twosuperimposed linear grating patterns are orthogonal with respect to oneanother and lie substantially in a vertical plane, and wherein thereticle is rotated in the vertical plane at approximately a 45° anglefrom a horizontal plane.
 21. An apparatus for detecting aberrations inan object system as manifested in a wavefront from the object system,comprising: a. a reticle positioned in a path of the wavefront, whereinthe reticle comprises two superimposed linear grating patterns; b. atleast one light detector positioned relative to the reticle to receive aself-image of at least one diffraction-caused pattern associated withthe wavefront; and c. at least one processor receiving signals from thelight detector representative of the self-image and deriving derivativesassociated therewith, the processor using the derivatives to determinethe aberrations, d. wherein the processor receives a frequencytransformation of the wavefront and derives derivatives associated withphases of the frequency transformation, the processor determiningderivatives of phases in two directions.
 22. The system of claim 21,wherein at least one of the two superimposed linear grating patterns issegmented.
 23. The method of claim 22, wherein the two superimposedlinear grating patterns arc orthogonal with respect to one another. 24.The apparatus of claim 21, wherein the processor fits a set of knownderivatives to the derivatives determined by the processor to obtaincoefficients of polynomials representative of the aberrations.
 25. Theapparatus of claim 24, wherein only selected portions in a spatialfrequency domain are used to determine coefficients.
 26. The apparatusof claim 21, wherein the object system is an eye.
 27. The apparatus ofclaim 26, wherein the two superimposed linear grating patterns areorthogonal with respect to one another and lie substantially in avertical plane, and wherein the reticle is rotated in the vertical planeat approximately a 45° angle from a horizontal plane.
 28. A method fordetermining aberrations in a reflective or internally reflective object,comprising; a. passing a light beam from the object through a reticle,wherein the reticle comprises two superimposed linear grating patterns;b. determining directional derivatives associated with the light beamsubsequent to the light beam passing through the reticle; and c. usingthe derivatives to output a measure of aberrations in the light beamand, hence, the object.
 29. The method of claim 28, wherein at least oneof the two superimposed linear grating patterns is segmented.
 30. Themethod of claim 29, wherein the two superimposed linear grating patternsare orthogonal with respect to one another.
 31. The method of claim 28,wherein the object is an eye.
 32. The method of claim 31 wherein the twosuperimposed linear grating patterns are orthogonal with respect to oneanother and lie substantially in a vertical plane, and wherein thereticle is rotated in the vertical plane at approximately a 45° anglefrom a horizontal plane.
 33. The method of claim 31, further comprisingtransforming a wavefront associated with the light beam from a spatialimage domain into a spatial frequency domain.
 34. The method of claim33, further comprising determining coefficients of polynomials based onthe direction derivatives.
 35. The method of claim 34, wherein the actof determining derivatives includes determining derivatives of phases ofthe wavefront.
 36. The method of claim 35, comprising determiningdirectional derivatives in at least two directions.
 37. The method ofclaim 36, wherein the coefficients are determined by fitting derivativesof a set of known polynomials to data obtained during the determiningact.
 38. A system for determining the shape of an electromagneticwavefront, comprising: a reticle positioned in a path of the wavefrontto be analyzed, wherein the reticle comprises two superimposed lineargrating patterns; at least one detector positioned to detect thewavefront passing through the reticle, the detector being substantiallylocated at a diffraction pattern self-imaging plane relative to thereticle; and at least one processor receiving an output signal from thelight detector and calculating the shape of the wavefront based thereon.39. The system of claim 38, wherein at least one of the two superimposedlinear grating patterns is segmented.
 40. The system of claim 39,wherein the two superimposed linear grating patterns are orthogonal withrespect to one another.
 41. The system of claim 40, wherein the locationof the self imaging plane is a function of the wavelength of thewavefront and the spatial periodicity of the reticle.
 42. The system ofclaim 38, wherein said diffraction pattern self imaging plane is locatedin the near field a longitudinal distance of approximately$d = \left( \frac{n\; p^{2}}{\lambda} \right)$ from said reticle,wherein p is the grating spacing of the grating,λ is the spectralwavelength of the wavefront, and n is an integer.
 43. The system ofclaim 38, wherein the at least one processor executes logic to undertakemethod acts comprising determining directional derivatives of theelectromagnetic wavefront.
 44. The system of claim 43, wherein themethod acts further include transforming a diffraction pattern of thewavefront at the detector from a spatial image domain into a spatialfrequency domain, prior to the act of determining coefficients.
 45. Thesystem of claim 44, wherein selected portions in the spatial frequencydomain are used to determine said coefficients.
 46. The system of claim43, wherein the method acts include determining coefficients ofpolynomials based on at least one gradient of a phase-front of thewavefront, the coefficients being representative of the shape of thewavefront.
 47. The system of claim 46, wherein the coefficients aredetermined by fitting derivative functions of a set of known polynomialsto the derivatives obtained during the determining act.
 48. The systemof claim 38, wherein directional derivatives are determined in at leasttwo directions.
 49. The system of claim 38, wherein said method actsfurther comprise implementing a computational matte screen for filteringout noise.
 50. The system of claim 38, wherein the wavefront isreflected from an eye and the shape of the wavefront is effected by theshape of the eye.
 51. The system of claim 50, wherein the twosuperimposed linear grating patterns are orthogonal with respect to oneanother and lie substantially in a vertical plane, and wherein thereticle is rotated in the vertical plane at approximately a 45° anglefrom a horizontal plane.
 52. A method for determining aberrations in anoptical system comprising at least one optical element, said methodcomprising: a. propagating a test beam along a path with said opticalsystem in said path of said test beam so as to he illuminated by saidtest beam; b. inserting a reticle in said path of said test beam at alocation with respect to said optical system so as to receive light fromsaid optical system, said light propagating through said reticle, andwherein the reticle comprises two superimposed linear grating patterns;and c. determining directional derivatives associated with said lightsubsequent to passing through the reticle; and using the derivatives tooutput a measure of said aberrations.
 53. The method of claim 52,wherein at least one of the two superimposed linear grating patterns issegmented.
 54. The method of claim 53, wherein the two superimposedsegmented linear grating patterns are orthogonal with respect to oneanother.
 55. The method of claim 53, further comprising transforming adiffraction pattern produced by said light passing through said reticlefrom a spatial image into a spatial frequency distribution.
 56. Themethod of claim 53, further comprising determining coefficients ofpolynomials based on the directional derivatives.
 57. The method ofclaim 56, wherein the coefficients arc determined by fitting derivativesof a set of known polynomials to data obtained during the determiningact.
 58. The method of claim 56, comprising determining directionalderivatives in at least two directions.
 59. The method of claim 56,comprising locating a light detector at a position in said path so as toreceive a self-image of the reticle.
 60. The method of claim 56, furthercomprising implementing a computational matte screen as a filter. 61.The method of claim 52, wherein the optical system is an eye.
 62. Themethod of claim 61, wherein the two superimposed linear grating patternsare orthogonal with respect to one another and lie substantially in avertical plane, and wherein the reticle is rotated in the vertical planeat approximately a 45° angle from a horizontal plane.
 63. An apparatusfor characterizing an object with a wavefront from the object,comprising: a reticle positioned in a path of the wavefront, the reticlecomprising two superimposed linear grating patterns; at least one lightdetector positioned relative to the reticle to receive a self-imagediffraction pattern of the reticle produced by the wavefront; and atleast one processor receiving signals from the light detectorrepresentative of the self-image diffraction pattern and derivingderivatives associated therewith, the processor using the derivatives tocharacterize said object.
 64. The apparatus of claim 63, wherein atleast one of the two superimposed linear grating patterns is segmented.65. The apparatus of claim 63, wherein the two superimposed segmentedlinear grating patterns are orthogonal with respect to one another. 66.The apparatus of claim 63, wherein the object is an eye.
 67. Theapparatus of claim 66 wherein the two superimposed linear gratingpatterns are orthogonal with respect to one another and liesubstantially in a vertical plane, and wherein the reticle is rotated inthe vertical plane at approximately a 45° angle from a horizontal plane.68. The apparatus of claim 63, wherein the location of the reticle isrelated to the wavelength of the wavefront and spatial frequency of thereticle.
 69. The apparatus of claim 63, wherein the processor producesfrequency transformation of the wavefront to produce a distribution infrequency space and derives derivatives of phases of the wavefront fromthe distribution in frequency space.
 70. The apparatus of claim 63,wherein the processor determines derivatives of phases in twodirections.
 71. The apparatus of claim 63, wherein the processor fits aset of known derivatives to the derivatives determined by the processorto obtain coefficients of polynomials representative of the aberrations.72. A method for determining aberrations in a reflective or internallyreflective object system, comprising: a. passing a light beam from theobject system through a reticle, said light beam producing a near fielddiffraction pattern at a Talbot plane, wherein the reticle comprises twosuperimposed linear grating patterns; b. imaging said near fielddiffraction pattern at said Talbot plane; c. using said near fielddiffraction pattern to output a measure of aberrations in the lightbeam.
 73. The method of claim 72, wherein at least one of the twosuperimposed linear grating patterns is segmented.
 74. The method ofclaim 73, wherein the two superimposed linear grating patterns areorthogonal with respect to one another.
 75. The method of claim 72,wherein the object system is an eye and said method is for determiningabeffation in said eye.
 76. The method of claim 75, wherein the twosuperimposed linear grating patterns are orthogonal with respect to oneanother and lie substantially in a vertical plane, and wherein thereticle is rotated in the vertical plane at approximately a 45° anglefrom a horizontal plane.
 77. The method of claim 72, further comprisingtransforming a wavefront associated with the light beam from a spatialimage domain into a spatial frequency domain.
 78. The method of claim77, wherein only selected portions in said spatial frequency domain areused to determine coefficients.
 79. The method of claim 72, furthercomprising locating a light detector at said Talbot plane to detect thenear field diffraction pattern.
 80. The method of claim 72, furthercomprising designing coffective optics based on said measure ofaberrations in said light beam so as to reduce said aberrations.
 81. Themethod of claim 72, wherein the object system comprises an eye.
 82. Themethod of claim 81, wherein the two superimposed linear grating patternsare orthogonal with respect to one another and lie substantially in avertical plane, and wherein the reticle is rotated in the vertical planeat approximately a 45° angle from a horizontal plane.
 83. The method ofclaim 72 wherein the reticle comprises a grating spacing, p, ofapproximately 50 micrometers, the talbot plane is located atapproximately a distance, d, between 2.9 to 3.0 millimeters from theobject system, or integer multiple thereof, and a wavelength of thelight beam is approximately 850 nanometers.
 84. The method of claim 72wherein the object system comprises an eye, the method furthercomprising using the measured aberrations to determine a visionprescription for the eye.
 85. The method of claim 84 further comprisingcreating a corrective lens that corrects for only low order aberrationsof the eye.
 86. The method of claim 84 further comprising creating acorrective lens that corrects for both low and high order aberrations ofthe eye.
 87. A method for making a corrective lens for correctingabenations in an eye, comprising: a. passing a light beam reflected fromthe eye through a reticle, said light beam producing a near fielddiffraction pattern at a self imaging plane, wherein the reticlecomprises two superimposed linear grating patterns; b. imaging said nearfield diffraction pattern at said self imaging plane; c. using said nearfield diffraction pattern to output a measure of aberrations in thelight beam; and d. using the measured abenations to create thecorrective lens.
 88. The method of claim 87, wherein at least one of thetwo superimposed linear grating patterns is segmented.
 89. The method ofclaim 88, wherein the two superimposed linear grating patterns areorthogonal with respect to one another.
 90. The method of claim 87wherein the two superimposed linear grating patterns are orthogonal withrespect to one another and lie substantially in a vertical plane, andwherein the reticle is rotated in the vertical plane at approximately a45° angle from a horizontal plane.
 91. The method of claim 87 whereinthe corretive lens corrects for only low order abenations of the eye.92. The method of claim 87 wherein the corrective lens corrects for bothlow and high order aberrations of the eye.